Hebrew - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Hebrew Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

πŸ“‹ Repository Contents

Models & Assets

  • Tokenizers (8k, 16k, 32k, 64k)
  • N-gram models (2, 3, 4, 5-gram)
  • Markov chains (context of 1, 2, 3, 4 and 5)
  • Subword N-gram and Markov chains
  • Embeddings in various sizes and dimensions (aligned and unaligned)
  • Language Vocabulary
  • Language Statistics

Performance Dashboard

Analysis and Evaluation


1. Tokenizer Evaluation

Tokenizer Compression

Tokenizer Fertility

Tokenizer OOV

Total Tokens

Results

Vocab Size Compression Avg Token Len UNK Rate Total Tokens
8k 3.129x 3.13 0.0482% 4,188,199
16k 3.502x 3.50 0.0540% 3,742,094
32k 3.872x 3.87 0.0597% 3,384,734
64k 4.191x πŸ† 4.19 0.0646% 3,127,199

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: ΧΧ™Χ™Χ–Χ Χ©Χ˜Χ™Χ™ΧŸ או ΧΧ™Χ–Χ Χ©Χ˜Χ™ΧŸ (Eisenstein), שם ΧžΧ©Χ€Χ—Χ” Χ’Χ¨ΧžΧ Χ™ ושם Χ™Χ”Χ•Χ“Χ™ אשכנזי Χ Χ€Χ•Χ₯. Χ€Χ™Χ¨Χ•Χ©...

Vocab Tokens Count
8k ▁אייז Χ Χ©Χ˜Χ™Χ™ΧŸ ▁או ▁איז Χ  שט Χ™ΧŸ ▁( e is ... (+26 more) 36
16k ▁אייז Χ Χ©Χ˜Χ™Χ™ΧŸ ▁או ▁איז נשט Χ™ΧŸ ▁( e is en ... (+20 more) 30
32k ▁אייז Χ Χ©Χ˜Χ™Χ™ΧŸ ▁או ▁איז נשט Χ™ΧŸ ▁( e is en ... (+19 more) 29
64k β–ΧΧ™Χ™Χ–Χ Χ©Χ˜Χ™Χ™ΧŸ ▁או ▁איז נשט Χ™ΧŸ ▁( e is enstein ), ... (+17 more) 27

Sample 2: Χ©Χ˜Χ™Χ‘Χœ היא Χ¦Χ•Χ¨Χͺ Χ”Χ§Χ˜Χ Χ” של Χ”ΧžΧ™ΧœΧ” Χ”Χ™Χ™Χ“Χ™Χͺ Χ©Χ˜Χ•Χ‘ ("Χ‘Χ™Χͺ" או "Χ—Χ“Χ¨"). ΧžΧ©Χ€Χ—Χ” ΧžΧ©Χ€Χ—Χ” אשכנזיים

Vocab Tokens Count
8k β–Χ©Χ˜ Χ™Χ‘Χœ ▁היא ▁צורΧͺ β–Χ”Χ§Χ˜Χ Χ” β–Χ©Χœ β–Χ”ΧžΧ™ΧœΧ” ▁הי Χ™Χ“Χ™Χͺ β–Χ©Χ˜ ... (+13 more) 23
16k β–Χ©Χ˜ Χ™Χ‘Χœ ▁היא ▁צורΧͺ β–Χ”Χ§Χ˜Χ Χ” β–Χ©Χœ β–Χ”ΧžΧ™ΧœΧ” ▁הי Χ™Χ“Χ™Χͺ β–Χ©Χ˜ ... (+12 more) 22
32k β–Χ©Χ˜ Χ™Χ‘Χœ ▁היא ▁צורΧͺ β–Χ”Χ§Χ˜Χ Χ” β–Χ©Χœ β–Χ”ΧžΧ™ΧœΧ” ▁הי Χ™Χ“Χ™Χͺ β–Χ©Χ˜ ... (+11 more) 21
64k β–Χ©Χ˜Χ™Χ‘Χœ ▁היא ▁צורΧͺ β–Χ”Χ§Χ˜Χ Χ” β–Χ©Χœ β–Χ”ΧžΧ™ΧœΧ” ▁היידיΧͺ β–Χ©Χ˜ Χ•Χ‘ ▁(" ... (+9 more) 19

Sample 3: ΧœΧΧ•Χ€Χ¨Χ“ הוא Χ”ΧͺΧ’ΧͺΧ™Χ§ Χ”Χ’Χ‘Χ¨Χ™ ΧœΧžΧ™ΧœΧ” Leopard, Χ”Χ§Χ™Χ™ΧžΧͺ Χ‘ΧžΧ‘Χ€Χ¨ Χ©Χ€Χ•Χͺ Χ•ΧžΧ©ΧžΧ’Χ•ΧͺΧ” היא נמר (Χ‘Χ’Χœ Χ—...

Vocab Tokens Count
8k β–ΧœΧ Χ•Χ€Χ¨ Χ“ ▁הוא ▁הΧͺ Χ’ΧͺΧ™Χ§ ▁הגברי β–ΧœΧž Χ™ΧœΧ” ▁le ... (+21 more) 31
16k β–ΧœΧ Χ•Χ€Χ¨ Χ“ ▁הוא ▁הΧͺ Χ’ΧͺΧ™Χ§ ▁הגברי β–ΧœΧžΧ™ΧœΧ” ▁le op ... (+17 more) 27
32k β–ΧœΧΧ•Χ€Χ¨ Χ“ ▁הוא ▁הΧͺ Χ’ΧͺΧ™Χ§ ▁הגברי β–ΧœΧžΧ™ΧœΧ” ▁le op ard ... (+15 more) 25
64k β–ΧœΧΧ•Χ€Χ¨ Χ“ ▁הוא ▁הΧͺΧ’ΧͺΧ™Χ§ ▁הגברי β–ΧœΧžΧ™ΧœΧ” ▁le opard , β–Χ”Χ§Χ™Χ™ΧžΧͺ ... (+12 more) 22

Key Findings

  • Best Compression: 64k achieves 4.191x compression
  • Lowest UNK Rate: 8k with 0.0482% unknown tokens
  • Trade-off: Larger vocabularies improve compression but increase model size
  • Recommendation: 32k vocabulary provides optimal balance for production use

2. N-gram Model Evaluation

N-gram Perplexity

N-gram Unique

N-gram Coverage

Results

N-gram Variant Perplexity Entropy Unique N-grams Top-100 Coverage Top-1000 Coverage
2-gram Word 839,907 19.68 4,883,996 3.8% 9.8%
2-gram Subword 388 πŸ† 8.60 45,811 57.3% 98.0%
3-gram Word 2,460,970 21.23 7,456,944 1.9% 5.1%
3-gram Subword 4,159 12.02 320,573 19.8% 57.8%
4-gram Word 6,086,424 22.54 12,242,689 1.3% 3.3%
4-gram Subword 31,153 14.93 1,768,539 7.8% 25.6%
5-gram Word 5,115,710 22.29 8,563,842 1.1% 3.0%
5-gram Subword 174,825 17.42 6,204,970 3.7% 13.2%

Top 5 N-grams by Size

2-grams (Word):

Rank N-gram Count
1 גל Χ™Χ“Χ™ 619,385
2 קישורים חיצוניים 326,599
3 Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ 252,301
4 ארצוΧͺ Χ”Χ‘Χ¨Χ™Χͺ 176,732
5 גל Χ€Χ™ 148,464

3-grams (Word):

Rank N-gram Count
1 קישורים חיצוניים Χ”Χ’Χ¨Χ•Χͺ 115,186
2 חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ 115,178
3 של ארצוΧͺ Χ”Χ‘Χ¨Χ™Χͺ 67,555
4 של Χ”ΧžΧΧ” Χ” 45,554
5 Χ”ΧžΧΧ” Χ” 20 39,531

4-grams (Word):

Rank N-gram Count
1 קישורים חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ 115,165
2 של Χ”ΧžΧΧ” Χ” 20 24,487
3 שבהם ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” אינה 19,413
4 ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” אינה מΧͺΧΧ™ΧžΧ” 19,413
5 אΧͺ Χ”Χ•Χ€Χ’Χͺ Χ”Χ‘Χ›Χ•Χ¨Χ” Χ©ΧœΧ• 16,388

5-grams (Word):

Rank N-gram Count
1 שבהם ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” אינה מΧͺΧΧ™ΧžΧ” 19,413
2 גרך אΧͺ Χ”Χ•Χ€Χ’Χͺ Χ”Χ‘Χ›Χ•Χ¨Χ” Χ©ΧœΧ• 11,486
3 Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ שבהם ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” 10,724
4 Χ©Χ•ΧœΧ™Χ™Χ שבהם ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” אינה 10,724
5 Χ‘Χ™Χͺ הנבחרים של ארצוΧͺ Χ”Χ‘Χ¨Χ™Χͺ 7,604

2-grams (Subword):

Rank N-gram Count
1 _ Χ” 39,073,833
2 Χͺ _ 29,026,407
3 _ Χ‘ 24,932,558
4 Χ” _ 24,128,474
5 ם _ 21,592,884

3-grams (Subword):

Rank N-gram Count
1 Χ™ ם _ 13,358,320
2 Χ• Χͺ _ 11,186,966
3 Χͺ _ Χ” 8,271,610
4 _ ש ל 6,687,390
5 ש ל _ 5,737,360

4-grams (Subword):

Rank N-gram Count
1 _ ש ל _ 5,452,714
2 _ א Χͺ _ 2,964,460
3 Χ• Χͺ _ Χ” 2,726,223
4 _ ג ל _ 2,650,017
5 Χ™ Χ™ ם _ 2,272,182

5-grams (Subword):

Rank N-gram Count
1 _ Χ© ל _ Χ” 1,545,782
2 _ Χ” Χ• א _ 1,326,505
3 _ א Χͺ _ Χ” 1,316,470
4 Χ” _ Χ© ל _ 1,085,085
5 Χ• _ Χ© ל _ 843,378

Key Findings

  • Best Perplexity: 2-gram (subword) with 388
  • Entropy Trend: Decreases with larger n-grams (more predictable)
  • Coverage: Top-1000 patterns cover ~13% of corpus
  • Recommendation: 4-gram or 5-gram for best predictive performance

3. Markov Chain Evaluation

Markov Entropy

Markov Contexts

Markov Branching

Results

Context Variant Avg Entropy Perplexity Branching Factor Unique Contexts Predictability
1 Word 1.1002 2.144 22.34 2,985,722 0.0%
1 Subword 0.8730 1.831 7.49 25,039 12.7%
2 Word 0.3737 1.296 2.25 66,677,134 62.6%
2 Subword 0.6573 1.577 4.43 187,480 34.3%
3 Word 0.1205 1.087 1.25 150,136,299 87.9%
3 Subword 0.6833 1.606 3.99 829,497 31.7%
4 Word 0.0427 πŸ† 1.030 1.07 187,719,110 95.7%
4 Subword 0.6743 1.596 3.51 3,312,743 32.6%

Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

Context Size 1:

  1. של Χ”Χ™Χ¦Χ™Χ’ Χ”Χ™Χ• ΧžΧ€Χ‘Χ™Χ§Χ™Χ ΧœΧ’Χ‘Χ•Χ“ Χ›ΧžΧ›Χ•Χ ΧΧ™ Χ¨Χ›Χ‘ Χ©Χ’Χ‘Χ¨Χ• ΧœΧ€Χ•Χ¨Χ˜ΧœΧ Χ“ ΧžΧ™Χ™ΧŸ Χ•Χ©Χ¨Χ“ Χ¨Χ•Χ—Χ•Χͺ Χ”ΧΧ§ΧœΧ™Χ€Χ‘ שם Χ”Χ©Χ™Χ¨ Χ”Χ€Χ©Χ•Χ˜
  2. אΧͺ Χ‘Χ’ΧŸ ΧΧœΧ•Χ£ ΧΧœΧ” ΧΧ˜ΧœΧ Χ˜Χ™Χͺ ΧœΧΧ—Χ¨ Χ”Χ€Χ‘Χ§Χ” ΧžΧ”Χ Χ•Χ¨ΧžΧ” איבוף Χ”ΧžΧ™Χ“Χ’ Χ©ΧœΧ• Χ•Χ›ΧŸ מגל Χ©Χ›Χ‘Χ” ΧΧ¨Χ›ΧΧ•ΧœΧ•Χ’Χ™Χͺ Χ‘ΧžΧ—Χ Χ”
  3. גל ΧžΧ¦Χ“Χ” Χ”Χ©ΧžΧΧœΧ™ ΧžΧ—Χ–Χ™Χ§ באזרחוΧͺ Χ¦Χ¨Χ€ΧͺΧ™Χͺ Χ’Χ¨Χ‘Χ™Χͺ ΧœΧ€Χ™Χ” Χ Χ™Χͺן למרלן Χ“Χ™Χ˜Χ¨Χ™Χš Χ‘Χ‘Χ™Χ§Χ•Χ¨ Χ‘Χ”Χ•Χ“Χ• נאבקו ΧœΧžΧ¦Χ•Χ ΧͺΧ©Χ•Χ‘Χ•Χͺ

Context Size 2:

  1. גל Χ™Χ“Χ™ ΧžΧ—Χ©Χ‘ Χ•Χ‘Χ›Χš ΧœΧ”Χ‘Χ™Χ¨ אΧͺ Χ©ΧœΧ˜Χ•ΧŸ Χ”Χ˜Χ¨Χ•Χ¨ ΧžΧ¨Χ“Χ›Χ™ ΧžΧ™Χ¨Χ¨Χ’ Χ‘ Χ—Χ–Χ Χ” של Χ”Χ’Χ™Χ¨ Χ Χ”Χ€Χ›Χ• ללא Χ¨ΧœΧ•Χ•Χ Χ˜Χ™Χ•Χͺ
  2. קישורים חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ Χ™ΧœΧ™Χ“Χ™ אוקראינה Χ‘Χ’ΧœΧͺ Χ§Χ•Χœ Χ‘Χ•Χ€Χ¨ΧŸ אלט Χ˜Χ Χ•Χ¨ ΧžΧ§Χ”ΧœΧ”sing unto godאלט Χ˜Χ Χ•Χ¨ Χ‘Χ•Χ€Χ¨...
  3. Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ Χ›Χ“Χ•Χ¨Χ’Χœ Χ‘Χ’Χ•Χ“Χ™Χ•Χͺ ΧžΧ•Χ’Χ“Χ•Χ Χ™ Χ›Χ“Χ•Χ¨Χ’Χœ באזור Χ›Χ•Χ¨Χ“Χ™Χ‘Χ˜ΧŸ שבגיראק גם Χ§Χ”Χ™ΧœΧ•Χͺ האם Χ©ΧœΧ”ΧŸ אף Χ™Χ•ΧͺΧ¨ ΧžΧ”Χ‘Χ™Χ¨Χ•Χ‘...

Context Size 3:

  1. קישורים חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ קנדים Χ”Χ—Χ‘Χ¨Χ” Χ”ΧžΧœΧ›Χ•ΧͺΧ™Χͺ זרים Χ‘Χ—Χ‘Χ¨Χ” Χ”ΧžΧœΧ›Χ•ΧͺΧ™Χͺ יהודים Χ‘Χ—Χ‘Χ¨Χ” Χ”ΧžΧœΧ›Χ•ΧͺΧ™Χͺ Χ”ΧžΧ“ΧœΧ™Χ” ...
  2. חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ Χ§Χ•ΧœΧ Χ•Χ’ Χ•Χ˜ΧœΧ•Χ•Χ™Χ–Χ™Χ” Χ¦ Χ™ΧœΧ™ΧΧ Χ™Χ•Χͺ ΧͺΧ§Χ©Χ•Χ¨Χͺ Χ¦ Χ™ΧœΧ™ΧΧ Χ™Χ Χ˜ΧœΧ•Χ•Χ™Χ–Χ™Χ” Χ¦ Χ™ΧœΧ™ΧΧ Χ™Χ Χ§Χ•ΧœΧ Χ•Χ’ Χ•Χ˜ΧœΧ•Χ•Χ™Χ–...
  3. של ארצוΧͺ Χ”Χ‘Χ¨Χ™Χͺ Χ‘Χ”ΧͺΧ‘Χ‘Χ‘ גל בקרים גל Χ”Χ§Χ¨Χ§Χ’ Χ•Χ’Χœ ΧͺΧ¦ΧœΧ•ΧžΧ™ אוויר Χ©Χ¦Χ•ΧœΧžΧ• ΧžΧžΧ˜Χ•Χ‘Χ™ ΧžΧ©ΧœΧ—Χͺ Χ”Χ—Χ§Χ¨ Χ”ΧΧ Χ˜ΧΧ¨Χ§Χ˜Χ™Χͺ Χ”Χ‘Χ¨Χ™Χ˜Χ™Χͺ...

Context Size 4:

  1. קישורים חיצוניים Χ”Χ’Χ¨Χ•Χͺ Χ©Χ•ΧœΧ™Χ™Χ ΧžΧ‘Χ“Χ¨ Χ’ΧžΧ™ΧͺΧ™ Χ”Χ›Χ‘Χ•Χ“ ΧΧ Χ’ΧœΧ™Χ ΧΧ Χ’ΧœΧ™Χ ΧžΧžΧ•Χ¦Χ Χ•ΧœΧ©Χ™ Χ©Χ Χ•ΧœΧ“Χ•
  2. של Χ”ΧžΧΧ” Χ” 20 Χ”Χ Χ€Χ™Χ§Χ• ΧžΧ Χ™Χ•Χͺ Χ•Χ Χ¨Χ©ΧžΧ• ΧœΧžΧ‘Χ—Χ¨ Χ‘Χ‘Χ•Χ¨Χ‘Χ” Χ’Χ©Χ¨Χ•Χͺ Χ—Χ‘Χ¨Χ•Χͺ ΧžΧ™Χ©Χ¨ΧΧœ Χ‘Χ™ΧŸ השאר ΧΧžΧ‘ΧœΧ™Χ™Χ– Χ”Χ•Χ Χ€Χ§Χ” ΧœΧ¨ΧΧ©Χ•Χ Χ” Χ‘Χ‘Χ•...
  3. שבהם ΧͺΧ‘Χ Χ™Χͺ Χ‘Χ¨Χ™Χ˜Χ Χ™Χ§Χ” אינה מΧͺΧΧ™ΧžΧ” Χ€Χ™Χ–Χ™Χ§ΧœΧ™Χ™Χ Χ—Χ‘Χ¨Χ™ ΧžΧžΧ“Χ™Χ של ΧžΧ’Χ’ΧœΧ™Χ Χ—Χ©ΧžΧœΧ™Χ™Χ

Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

Context Size 1:

  1. _Χ’ΧœΧ˜Χ•ΧΧ_קרוריזם_
  2. Χ™Χ§Χ¨Χ•._Χ§Χ•ΧΧ•Χœ_Χ”Χ™ΧžΧ—
  3. Χ•Χ—Χ•Χͺוריהדיגם_שלך

Context Size 2:

  1. _Χ”Χ¨ΧΧœΧ₯,_Χ•Χ™ΧŸ._Χ‘Χ›Χ•Χͺ
  2. Χͺ_Χ‘Χ”_Χ”Χ©ΧžΧ•Χ“_Χ”ΧžΧ—Χ–Χ§_
  3. _Χ‘Χ—Χ¨Χ•,_אΧͺ_מא/Χ Χ§Χ¨Χͺ

Context Size 3:

  1. ים_דיאנה_ΧͺΧ•Χ›ΧŸ_Χ¨Χ§Χ•Χ‘
  2. Χ•Χͺ_Χ‘Χ¦Χ™Χ”_Χ™Χ©Χ¨ΧΧœΧ™Χ€Χ•Χ¨Χ™
  3. Χͺ_Χ”ΧžΧ§Χ™Χ™Χ Χͺ_45_Χ“ΧΧ•ΧœΧ•

Context Size 4:

  1. _של_חיים)_Χ©ΧžΧ—Χ•Χ₯_ΧœΧ“Χ—
  2. _אΧͺ_Χ›ΧœΧœ_Χ‘ΧžΧ’Χ–Χ™ΧŸ_Χ”Χ˜Χ¨Χ™
  3. Χ•Χͺ_Χ”Χ¨ΧΧ©Χ•ΧŸ_Χ”Χ™Χ©Χ™Χ‘Χ”_Χ‘Χ™

Key Findings

  • Best Predictability: Context-4 (word) with 95.7% predictability
  • Branching Factor: Decreases with context size (more deterministic)
  • Memory Trade-off: Larger contexts require more storage (3,312,743 contexts)
  • Recommendation: Context-3 or Context-4 for text generation

4. Vocabulary Analysis

Zipf's Law

Top Words

Coverage Curve

Statistics

Metric Value
Vocabulary Size 1,343,537
Total Tokens 218,728,300
Mean Frequency 162.80
Median Frequency 5
Frequency Std Dev 6864.53

Most Common Words

Rank Word Frequency
1 של 5,459,894
2 אΧͺ 2,971,688
3 גל 2,703,880
4 הוא 1,339,510
5 גם 1,154,254
6 Χ‘ 905,656
7 Χ‘Χ©Χ Χͺ 775,632
8 Χ” 760,765
9 גם 682,600
10 Χ”Χ™Χ” 665,182

Least Common Words (from vocabulary)

Rank Word Frequency
1 markomannen 2
2 traditiones 2
3 possessionesque 2
4 bisterem 2
5 אנוויגאדו 2
6 Χ§Χ¨Χ•ΧΧ˜Χ™ΧͺΧΧ Χ˜Χ” 2
7 Χ§Χ¨Χ•ΧΧ˜Χ™ΧͺΧΧ™Χ•Χ•ΧŸ 2
8 ΧžΧ Χ“ΧΧ¨Χ™Χ₯ 2
9 בקבא׀אהו 2
10 בבקבא׀אהו 2

Zipf's Law Analysis

Metric Value
Zipf Coefficient 0.8691
RΒ² (Goodness of Fit) 0.995091
Adherence Quality excellent

Coverage Analysis

Top N Words Coverage
Top 100 18.7%
Top 1,000 39.8%
Top 5,000 60.2%
Top 10,000 69.8%

Key Findings

  • Zipf Compliance: RΒ²=0.9951 indicates excellent adherence to Zipf's law
  • High Frequency Dominance: Top 100 words cover 18.7% of corpus
  • Long Tail: 1,333,537 words needed for remaining 30.2% coverage

5. Word Embeddings Evaluation

Embedding Isotropy

Similarity Matrix

t-SNE Words

t-SNE Sentences

5.1 Cross-Lingual Alignment

Alignment Quality

Multilingual t-SNE

5.2 Model Comparison

Model Dimension Isotropy Semantic Density Alignment R@1 Alignment R@10
mono_32d 32 0.8057 0.3812 N/A N/A
mono_64d 64 0.7873 0.2918 N/A N/A
mono_128d 128 0.7406 0.2357 N/A N/A
aligned_32d 32 0.8057 πŸ† 0.3678 0.1680 0.6000
aligned_64d 64 0.7873 0.2944 0.3600 0.7620
aligned_128d 128 0.7406 0.2283 0.4900 0.8080

Key Findings

  • Best Isotropy: aligned_32d with 0.8057 (more uniform distribution)
  • Semantic Density: Average pairwise similarity of 0.2999. Lower values indicate better semantic separation.
  • Alignment Quality: Aligned models achieve up to 49.0% R@1 in cross-lingual retrieval.
  • Recommendation: 128d aligned for best cross-lingual performance

6. Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

6.1 Productivity & Complexity

Metric Value Interpretation Recommendation
Productivity Index 5.000 High morphological productivity Reliable analysis
Idiomaticity Gap -0.772 Low formulaic content -

6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

Productive Prefixes

Prefix Examples
-Χ• Χ•Χ€Χ¨Χ™Χ‘Χ”, וחדאΧͺ, Χ•Χ”Χ‘Χ˜Χ•Χ“Χ Χ˜Χ™Χ
-Χ” Χ”Χ™Χ™Χ“Χ•ΧŸ, Χ”Χ‘Χ¨Χ‘Χ¨Χ™Χ–Χ¦Χ™Χ”, Χ”ΧΧ’Χ™Χ˜Χ˜Χ•Χ¨Χ™Χ
-מ ΧžΧžΧ’Χ™ΧŸ, ΧžΧœΧ‘Χ™Χ₯, ΧžΧ¨Χ’Χ©Χ™
-Χ‘ באנצ, Χ‘Χ”Χ¨ΧžΧ•Χ Χ™Χ§Χ•Χͺ, Χ‘Χ”ΧžΧœΧ¦Χͺ
-ל ΧœΧ‘Χ€Χ§Χ™, ΧœΧ”Χ‘Χ’Χ‘Χ¨Χ”, ΧœΧΧ™Χ¨Χ•Χ€Χ™Χ
-Χ© Χ©Χ”Χ˜ΧœΧ’Χ¨Χ£, Χ©Χ”ΧͺΧ™Χ•Χ’, Χ©Χ•ΧΧœΧ¨
-Χ•Χ” Χ•Χ”Χ‘Χ˜Χ•Χ“Χ Χ˜Χ™Χ, והראווה, Χ•Χ”Χ¨Χ™Χ‘Χͺ
-א ΧΧ™Χ˜Χ™Χ˜ΧΧ•Χ•Χ™, ΧΧ Χ˜Χ™Χ€Χ•Χ‘Χ•Χ€Χ•ΧœΧ™Χ€Χ™Χ“Χ™Χͺ, א֢צְבְּגוֹנִי

Productive Suffixes

Suffix Examples
-ם Χ•Χ”Χ‘Χ˜Χ•Χ“Χ Χ˜Χ™Χ, Χ”ΧΧ’Χ™Χ˜Χ˜Χ•Χ¨Χ™Χ, ΧœΧΧ™Χ¨Χ•Χ€Χ™Χ
-Χ” Χ›ΧžΧ•Χ›Χ”, Χ•Χ€Χ¨Χ™Χ‘Χ”, Χ”Χ‘Χ¨Χ‘Χ¨Χ™Χ–Χ¦Χ™Χ”
-Χͺ Χ Χ•Χ•Χ˜Χ•Χͺ, וחדאΧͺ, ΧΧ Χ˜Χ™Χ€Χ•Χ‘Χ•Χ€Χ•ΧœΧ™Χ€Χ™Χ“Χ™Χͺ
-ים Χ•Χ”Χ‘Χ˜Χ•Χ“Χ Χ˜Χ™Χ, Χ”ΧΧ’Χ™Χ˜Χ˜Χ•Χ¨Χ™Χ, ΧœΧΧ™Χ¨Χ•Χ€Χ™Χ
-Χ•Χͺ Χ Χ•Χ•Χ˜Χ•Χͺ, ׀רקיםאחיוΧͺ, Χ‘Χ”Χ¨ΧžΧ•Χ Χ™Χ§Χ•Χͺ
-Χ™ ΧΧ™Χ˜Χ™Χ˜ΧΧ•Χ•Χ™, Χ–Χ•ΧœΧ Χ‘Χ§Χ™, ΧœΧ‘Χ€Χ§Χ™
-ן Χ“Χ¨Χ™Χ’Χ™Χ˜Χ©Χ™ΧŸ, Χ”Χ™Χ™Χ“Χ•ΧŸ, ΧžΧžΧ’Χ™ΧŸ
-s lugares, wootens, hijras

6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

Stem Cohesion Substitutability Examples
ΧͺΧ€Χ§Χ™ 2.54x 314 contexts ΧͺΧ€Χ§Χ™Χ’, Χ‘ΧͺΧ€Χ§Χ™, ΧͺΧ€Χ§Χ™Χ¨
Χ•Χ€Χ™Χ’ 2.45x 92 contexts Χ•Χ€Χ™Χ’Χ”, ΧžΧ•Χ€Χ™Χ’, Χ”Χ•Χ€Χ™Χ’
Χ˜ΧœΧ•Χ• 2.81x 51 contexts Χ˜ΧœΧ•Χ•Χ‘, Χ˜ΧœΧ•Χ•Χ”, Χ˜ΧœΧ•Χ•Χ’
Χ’Χ™ΧœΧ• 1.93x 275 contexts Χ’Χ™ΧœΧ•Χͺ, Χ’Χ™ΧœΧ•Χ, Χ”Χ’Χ™ΧœΧ•
Χ’Χ¨ΧžΧ  2.21x 126 contexts Χ’Χ¨ΧžΧ Χ™, Χ’Χ¨ΧžΧ Χ”, Χ’Χ¨ΧžΧ Χ•
Χ™Χ¦Χ•Χ  2.23x 120 contexts Χ–Χ™Χ¦Χ•Χ Χ’, Χ—Χ™Χ¦Χ•Χ Χ”, Χ§Χ™Χ¦Χ•Χ Χ”
ΧͺΧ§Χ•Χ€ 2.13x 149 contexts ΧͺΧ§Χ•Χ€Χͺ, Χ‘ΧͺΧ§Χ•Χ€, ΧͺΧ§Χ•Χ€Χ”
ΧžΧ“Χ™Χ  1.90x 259 contexts ΧžΧ“Χ™Χ Χ, ΧžΧ“Χ™Χ Χͺ, ΧžΧ“Χ™Χ Χ¦
Χ§Χ™Χ™Χž 1.95x 203 contexts Χ§Χ™Χ™ΧžΧ•, Χ§Χ™Χ™ΧžΧ”, Χ§Χ™Χ™ΧžΧͺ
Χ•Χ’Χ¨Χ€ 1.73x 292 contexts Χ•Χ’Χ¨Χ€Χ”, Χ•Χ’Χ¨Χ€Χ™, Χ•Χ’Χ¨Χ€Χ•
ΧͺΧ•Χ›Χ  1.69x 272 contexts ΧͺΧ•Χ›Χ Χ”, Χͺוכנם, ΧͺΧ•Χ›Χ ΧŸ
Χ¨Χ‘Χ™Χ˜ 2.40x 45 contexts Χ‘Χ¨Χ‘Χ™Χ˜, Χ¨Χ‘Χ™Χ˜Χœ, Χ’Χ¨Χ‘Χ™Χ˜

6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

Prefix Suffix Frequency Examples
-Χ” -Χͺ 158 words Χ”ΧžΧ€ΧœΧ‘Χ•Χͺ, Χ”Χ”Χ–Χ“Χ•Χ•Χ’Χ•Χͺ
-Χ• -Χͺ 158 words Χ•Χ›ΧžΧ¨ΧΧ™Χ™Χ Χͺ, Χ•Χ‘ΧžΧ©ΧΧ™Χ•Χͺ
-Χ” -ם 154 words הגזברים, Χ”Χ˜ΧΧ˜ΧΧ¨Χ™Χ
-Χ• -ם 144 words וניכובם, וברצי׀ים
-Χ” -ים 136 words הגזברים, Χ”Χ˜ΧΧ˜ΧΧ¨Χ™Χ
-Χ• -Χ” 114 words Χ•Χͺראקיה, Χ•Χ•Χ Χ¨Χ”
-Χ• -ים 110 words וברצי׀ים, Χ•ΧžΧ™Χ™Χ‘Χ“Χ™Χ
-Χ• -Χ•Χͺ 105 words Χ•Χ‘ΧžΧ©ΧΧ™Χ•Χͺ, Χ•Χ¨Χ¦Χ™Χ•Χ ΧœΧ™Χ•Χͺ
-מ -ם 90 words ΧžΧžΧ—Χ Χ™Χ™Χ, ΧžΧ”Χ€ΧΧ¨Χ§Χ™Χ
-מ -Χͺ 85 words ΧžΧ”Χ§ΧœΧ•Χ¨Χ™Χ•Χͺ, מΧͺΧ’Χ©Χ¨Χͺ

6.5 Recursive Morpheme Segmentation

Using Recursive Hierarchical Substitutability, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., prefix-prefix-root-suffix).

Word Suggested Split Confidence Stem
sipstrassi sipstras-s-i 7.5 s
אברדינשייר אברדינשי-Χ™-Χ¨ 7.5 Χ™
Χ”ΧΧ Χ˜Χ™Χ Χ’Χ“Χ•Χ Χ©Χ™Χ™Χ¨ Χ”ΧΧ Χ˜Χ™Χ Χ’Χ“Χ•Χ Χ©Χ™-Χ™-Χ¨ 7.5 Χ™
Χ•Χ‘Χ‘Χ˜Χ Χ“Χ¨Χ˜Χ™Χ Χ•Χ‘-Χ‘Χ˜Χ Χ“Χ¨Χ˜-ים 6.0 Χ‘Χ˜Χ Χ“Χ¨Χ˜
Χ•ΧͺΧ™Χ Χ•Χ§Χ•ΧͺΧ™Χ”ΧŸ Χ•ΧͺΧ™Χ Χ•Χ§Χ•Χͺ-Χ™Χ”-ן 6.0 Χ•ΧͺΧ™Χ Χ•Χ§Χ•Χͺ
שבא׀שרוΧͺם Χ©Χ‘-א׀שרוΧͺ-ם 6.0 א׀שרוΧͺ
Χ”Χ©ΧͺΧ§Χ€Χ•Χ™Χ•Χͺיהם Χ”Χ©ΧͺΧ§Χ€Χ•Χ™Χ•Χͺ-Χ™Χ”-ם 6.0 Χ”Χ©ΧͺΧ§Χ€Χ•Χ™Χ•Χͺ
ΧžΧ€Χ¨Χ•Χ•Χͺיהם ΧžΧ€Χ¨Χ•Χ•Χͺ-Χ™Χ”-ם 6.0 ΧžΧ€Χ¨Χ•Χ•Χͺ
Χ•Χ”ΧΧ¨Χ›ΧΧ•ΧœΧ•Χ’Χ™Χ Χ•Χ”-ΧΧ¨Χ›ΧΧ•ΧœΧ•Χ’-ים 6.0 ΧΧ¨Χ›ΧΧ•ΧœΧ•Χ’
Χ”ΧͺΧ™Χ™Χ‘Χ©Χ•ΧͺΧ” Χ”ΧͺΧ™Χ™Χ‘Χ©-Χ•Χͺ-Χ” 6.0 Χ”ΧͺΧ™Χ™Χ‘Χ©
Χ’Χ§Χ¨Χ•Χ Χ•ΧͺΧ™Χ”ΧŸ Χ’Χ§Χ¨Χ•Χ Χ•Χͺ-Χ™Χ”-ן 6.0 Χ’Χ§Χ¨Χ•Χ Χ•Χͺ
Χ©Χ‘ΧžΧ“Χ‘Χ¨Χ™Χ•Χͺ Χ©Χ‘-ΧžΧ“Χ‘Χ¨Χ™-Χ•Χͺ 6.0 ΧžΧ“Χ‘Χ¨Χ™
ΧžΧ¨ΧΧ©Χ•Χ Χ™Χ•ΧͺΧ• ΧžΧ¨ΧΧ©Χ•Χ Χ™-Χ•Χͺ-Χ• 6.0 ΧžΧ¨ΧΧ©Χ•Χ Χ™
ΧžΧžΧ—ΧœΧ•Χͺיהם ΧžΧžΧ—ΧœΧ•Χͺ-Χ™Χ”-ם 6.0 ΧžΧžΧ—ΧœΧ•Χͺ
Χ”Χ€Χ Χ•ΧœΧ•Χ’Χ™Χ” Χ”-Χ€Χ Χ•ΧœΧ•Χ’-Χ™Χ” 6.0 Χ€Χ Χ•ΧœΧ•Χ’

6.6 Linguistic Interpretation

Automated Insight: The language Hebrew shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.


7. Summary & Recommendations

Performance Dashboard

Production Recommendations

Component Recommended Rationale
Tokenizer 64k BPE Best compression (4.19x)
N-gram 2-gram Lowest perplexity (388)
Markov Context-4 Highest predictability (95.7%)
Embeddings 100d Balanced semantic capture and isotropy

Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

Tokenizer Metrics

Compression Ratio

Definition: The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.

Intuition: Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.

What to seek: Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

Average Token Length (Fertility)

Definition: Mean number of characters per token produced by the tokenizer.

Intuition: Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.

What to seek: Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

Unknown Token Rate (OOV Rate)

Definition: Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.

Intuition: Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.

What to seek: Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

N-gram Model Metrics

Perplexity

Definition: Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.

Intuition: If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.

What to seek: Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

Entropy

Definition: Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.

Intuition: High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.

What to seek: Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

Coverage (Top-K)

Definition: Percentage of corpus occurrences explained by the top K most frequent n-grams.

Intuition: High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.

What to seek: Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

Markov Chain Metrics

Average Entropy

Definition: Mean entropy across all contexts, measuring average uncertainty in next-word prediction.

Intuition: Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).

What to seek: Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

Branching Factor

Definition: Average number of unique next tokens observed for each context.

Intuition: High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).

What to seek: Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

Predictability

Definition: Derived metric: (1 - normalized_entropy) Γ— 100%. Indicates how deterministic the model's predictions are.

Intuition: 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.

What to seek: Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

Vocabulary & Zipf's Law Metrics

Zipf's Coefficient

Definition: The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.

Intuition: A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.

What to seek: Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

RΒ² (Coefficient of Determination)

Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.

Intuition: RΒ² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.

What to seek: RΒ² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

Vocabulary Coverage

Definition: Cumulative percentage of corpus tokens accounted for by the top N words.

Intuition: Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.

What to seek: Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

Word Embedding Metrics

Isotropy

Definition: Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.

Intuition: High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.

What to seek: Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

Average Norm

Definition: Mean magnitude (L2 norm) of word vectors in the embedding space.

Intuition: Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.

What to seek: Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

Cosine Similarity

Definition: Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).

Intuition: Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.

What to seek: Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

t-SNE Visualization

Definition: t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.

Intuition: Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.

What to seek: Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

General Interpretation Guidelines

  1. Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
  2. Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
  3. Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
  4. Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
  5. Language-specific patterns: Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.

Visualizations Index

Visualization Description
Tokenizer Compression Compression ratios by vocabulary size
Tokenizer Fertility Average token length by vocabulary
Tokenizer OOV Unknown token rates
Tokenizer Total Tokens Total tokens by vocabulary
N-gram Perplexity Perplexity by n-gram size
N-gram Entropy Entropy by n-gram size
N-gram Coverage Top pattern coverage
N-gram Unique Unique n-gram counts
Markov Entropy Entropy by context size
Markov Branching Branching factor by context
Markov Contexts Unique context counts
Zipf's Law Frequency-rank distribution with fit
Vocab Frequency Word frequency distribution
Top 20 Words Most frequent words
Vocab Coverage Cumulative coverage curve
Embedding Isotropy Vector space uniformity
Embedding Norms Vector magnitude distribution
Embedding Similarity Word similarity heatmap
Nearest Neighbors Similar words for key terms
t-SNE Words 2D word embedding visualization
t-SNE Sentences 2D sentence embedding visualization
Position Encoding Encoding method comparison
Model Sizes Storage requirements
Performance Dashboard Comprehensive performance overview

About This Project

Data Source

Models trained on wikipedia-monthly - a monthly snapshot of Wikipedia articles across 300+ languages.

Project

A project by Wikilangs - Open-source NLP models for every Wikipedia language.

Maintainer

Omar Kamali - Omneity Labs

Citation

If you use these models in your research, please cite:

@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}

License

MIT License - Free for academic and commercial use.

Links


Generated by Wikilangs Models Pipeline

Report Date: 2026-01-13 14:18:23

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